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arXiv · 2604.28188

Cosmology of fractional gravity

Iván Salvador-García·Gianluca Calcagni
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Abstract

This is a first study of the cosmology of classical fractional gravity, a nonlocal proposal endowed with self-adjoint fractional d'Alembertian operators which serves as the basis for an ultraviolet-complete theory of quantum gravity. We derive the classical covariant nonlocal equations of motion for an arbitrary fractional exponent $\gamma$ and reduce them to the Friedmann equations on a homogeneous and isotropic cosmological background. We find that de Sitter is an exact stable solution and that bouncing exact solutions are sustained by phantom ($w<-1$) or ghost ($\rho<0$) fluids, in the latter case with a new type of finite-future singularity in the barotropic index. Different representations of the form factor give exactly the same solutions, thus confirming that the formulation of fractional field theories relies on a universality class of form factors. We compare these preliminary results with what obtained in multi-fractional cosmological models mimicking the spacetime geometry of fractional quantum gravity.

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Iván Salvador-García, Gianluca Calcagni. 2026-04-30. Cosmology of fractional gravity. https://doi.org/10.1088/1475-7516%2F2026%2F09%2F033

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